Part A

Answer the following questions about the provided GeoGebra application.

If we keep the center

$,$ what is the least amount of error that is generated between

and

$?$

Within this application, is there a "best" way to approximate

$?$ Explain.

Part B

Copy the following MATLAB text $($DOCX$)$ Download MATLAB text $($DOCX$)$ into MATLAB, which recreates this power series approximation of cosine but to greater precision than is possible in the GeoGebra application, and address the following questions.

If we keep the center LaTeX: a$=0,$ what is the least amount of error that is generated between

and

within the program, and how many terms are needed to achieve this error?

Keeping in mind that we $($like in the applet$)$ can only use centers taken from the unit circle, is there a best way to approximate

in the program?

If we keep the center LaTeX: a$=0,$ what is the least amount of error that is generated between LaTeX: P$(50)$ and LaTeX: $\backslash$cos$(50)$ within the program? Explain the cause for this error.

Keeping in mind that we $($like in the applet$)$ can only use centers taken from the unit circle, is there a best way to approximate

in the program?

Part C

Your group is required to devise the most efficient way to calculate

for any particular value of

$.$ Assuming you are first given the value of

$,$ give a method for determining the center and number of terms to make this efficient calculation, and justify why your group's given method is more efficient than other possible determinations of

and

$.$